Every family whose home was destroyed in the Grenfell Tower fire will receive a down-payment of at least £500 on Monday.
The Prime Minister has confirmed that each affected household is going to receive £500 in cash, as well as £5,000 delivered through the Department of Work and Pensions.
Downing Street says affected families can access the cash payment immediately from the council "as and when" they need it.
Number 10 has stressed that households who do not have a bank account will be given support to ensure they can access the rest of the down-payment.
Theresa May, who has faced criticism for her response to the tragedy in North Kensington, said: "As we continue to respond to the needs of the community, our focus is on ensuring that all of those affected by this unimaginable tragedy get the right support as quickly as possible.
"My government will continue to do absolutely everything possible to help all of those affected through the difficult days, weeks, months and years ahead."
The down-payment is part of a £5m support fund established by the Government in the wake of Wednesday's fire.
It is in addition to a guarantee of funding for temporary accommodation for the families unable to return to their homes, and funding for legal representation to ensure residents' voices are heard during a planned public inquiry.
There had been claims that some victims were being sent outside of the borough with just £10 a day to live on.
At Downing Street on Saturday, Theresa May met with 16 victims and volunteers from the local community - and those present said their harrowing accounts moved the Prime Minister to well up.
At least 58 people are missing and presumed dead in the blaze that broke out in the early hours, catching many families in their sleep.
The tragedy in a social housing complex in Britain's wealthiest borough has become a symbol of inequality in the country, stoking tensions after seven years of austerity.
The PM has ordered a public inquiry into the blaze, as the cladding used to insulate the tower block and the building's safety measures have come under scrutiny.
Chancellor Philip Hammond said the cladding, which has been blamed for spreading the fire, is banned in Britain.